This applet shows the predictions of the logistic map model of population dynamics.

Select different values of and and observe how the dynamics changes.
You should be able to identify at least the following behaviour: initially there is a transitional stage after which a stable phase sets in, in which

the population is extinct (for what values of this happens?), or

the population size remains constant at a value that depends on (for what values of this happens?), or

the population size oscillates between two values that depends on (for what values of this happens?), or

the population size oscillates among four values that depends on (for what values of this happens?), or

..., or

there is no regularity in the variation of population numerosity with respect to time.

In the next activity you will have an overall view of all of these behaviors.